How can migration threaten the EU?

I just couldn't wrap my head around the idea that migration could threaten the EU. Russia's nukes maybe though unlikely because of mutually assured destruction, Isis not so much yes ofcourse they can do major damage but a existential threat no way. An asteroid impact definately could destroy entire continents and we have no serious defenses. But let's stay on Earth. If migration is in fact a threat or if it can cause a political rift so significant that the EU would fall apart then why not just stop the boat people. It's really simple what is more important migration or the success of the EU. And this is regardless of whether we are pro or anti migration. Think about it. Or is the stopping of the boat people the real existential threat the EU keeps talking about?
Is this whole thing engineered?